Acoustoelastic scattering and attenuation in polycrystalline materials

Acoustoelasticity describes the phase velocity of a propagating wave in a nonlinear elastic material with a non-zero stress state. Traditionally, acoustoelasticity models assume that the wave propagates without energy loss or attenuating effects due to scattering or absorption of the wave in the material. However, scattering and attenuation effects are common in real metallic materials. In this case, the propagating medium for an ultrasonic wave consists of a continuous distribution of discrete grains with distinct orientations, i.e., a polycrystalline medium. The distinct orientations of the grains result in point to point differences in the elastic stiffness along the propagation path of the wave. The wave propagates with a phase velocity described by an average stiffness of the grains that have been previously in the propagation path. The next grain in the travel path will have a slightly different stiffness than the average and causes the grain boundary to scatter a portion of the wave\u27s energy in various directions. A non-zero stress state can significantly cause changes in the average elastic stiffness of the bulk material and the local elastic stiffness of individual grains. This causes the scattering in various directions and the total energy removed by scattering from the coherent wave to become stress dependent. Acoustoelastic scattering coefficients are derived that quantify the intensity of scattered energy for incoming and scattered waves. The incident and scattering directions are described in spherical coordinates allowing for many propagation and polarization configurations with respect to the direction of applied or residual stress. Both longitudinal and shear wave scattering is considered in polycrystalline materials containing grains with cubic crystallite elastic symmetry. The total scattered energy out of the wave is quantified as an acoustoelastic attenuation coefficient. Example results are presented for uniaxially stressed iron and aluminum. It is demonstrated that practical ultrasonic measurements based on scattering effects have better measurement resolution than traditional phase velocity measurements. Applications for the nondestructive evaluation of stressed structural components can be based on this theory